Hmm, so I've been lucky enough to get my hands on Final Fantasy Tactics for both the ps1 and the psp, and I've happened to have beaten both. While Tactics for PSP has better graphics and revamped dialog AND revamped moves... Some prefer the classic over the remake. Which at this point in time I think couldn't have come at a better time for the PSP as their marketing sales for the PSP haven't exactly been spectacular.
I personally find that Tactics is one of the best games to have came out of the Ps1 due to the fact that yes... it's a tactical game that sometimes verges on mundane and boring but it kept be interested for hours upon end. The only downfall is that shear magnitude of content in this classic game. Secret characters and amazing job classes, for one. But I dunno. Is the classic better? I'd probably say so only for the truely hardcore classic gamer fans. I recommend anybody with a PSP to get their hands on Final Fantasy Tactics : War of The Lions.
Final Fantasy Tactics: War of The Lion